In this work, we use an analytical approach to study the dynamic consequences of refuge use by the prey in the Rosenzweig-MacArthur predator-prey model with the refuge function proposed by Almanza-Vasquez. We will evaluate the effects with regard to the local stability of equilibrium points in the first quadrant. We show that there is a trend from limit cycles through non-zero stable points.

Here we study quadratic systems using certain Dulac functions and a geometric method.

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We show what physical capacity of refuge it influences in the existence and stability the unique equilibrium point at interior of the first quadrant. We analyze the consequences of such function through modifying the well-known Lotka-Volterra predator-prey model with prey self-limitation.

In this paper we construct an asymptotic for resonance of a wave function associated with the Klein-Gordon equation in presence of a potential barrier. To achieve this, we reduce the main differential equation to an integral equation using Green's function, Fourier transform and Neumann series.